Find all possible nonnegative quadruplets (a,b,c,d) that satisfy this equation:
2a + 6b + 9c = 11d
Prove that no further nonnegative solution to the given equation is possible.
(a, b, c, d)
(0, 0, 1, 1) 2^a + 6^b + 9^c = 11^d = 11
(2, 1, 0, 1) 2^a + 6^b + 9^c = 11^d = 11
(2, 2, 2, 2) 2^a + 6^b + 9^c = 11^d = 121
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import math
afactor = math.log(11)/math.log(2)
bfactor = math.log(11)/math.log(6)
cfactor = math.log(11)/math.log(9)
big = 50
solns = []
for d in range(1,big+1):
rhs = 11**d
amax = int(afactor * d)
bmax = int(bfactor * d)
cmax = int(cfactor * d)
for a in range(amax+1):
for b in range(bmax+1):
for c in range(cmax+1):
if 2**a + 6**b + 9**c == rhs:
print(2**a + 6**b + 9**c, 11**d, (a,b,c,d))
solns.append((a,b,c,d))
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Posted by Larry
on 2023-06-02 07:38:30 |
Computer solution without analytic proof
